Considere que duas substâncias, A e B, de massas respectivas mA e mB e calores específicos cA e cB, são colocadas em contato térmico sob condições em que a pressão é mantida constante. Considerando que, nesta pressão, os calores específicos e as massas das substâncias obedecem à relação mAcA = 3 mBcB e que antes do contato cada substância estava à temperatura TA e TB, respectivamente, pode-se afirmar que a temperatura final Tf após o equilíbrio térmico ser alcançado, é

Let's break down the problem step by step to find the correct answer.

The problem states that two substances, , A and B, with masses mA and mB, and specific heats cA and cB, respectively, are in thermal contact under constant pressure conditions. We are also given that, at this pressure, the specific heats and masses of the substances obey the relation mA cA = 3mB cB.

Before coming into contact, each substance was at a temperature TA and TB, respectively. We need to find the final temperature Tf after thermal equilibrium is reached.

To solve this problem, we can use the principle of heat exchange, which states that the heat gained by one substance is equal to the heat lost by the other substance.

Let's assume that the heat gained by substance A is Q. Then, the heat lost by substance B is also Q. We can write the heat gained by A as:

Q = mAcA (Tf - TA)

And the heat lost by B as:

Q = mBcB (TB - Tf)

Since Q is the same in both cases, we can equate the two expressions:

mAcA (Tf - TA) = mBcB (TB - Tf)

Now, we can use the given relation mA cA = 3mB cB to simplify the equation:

3mBcB (Tf - TA) = mBcB (TB - Tf)

Simplifying further, we get:

3Tf - 3TA = TB - Tf

Combining like terms, we get:

4Tf = 3TA + TB

Finally, dividing both sides by 4, we get the final temperature Tf:

Tf = {3TA + TB over 4}

Therefore, the correct answer is option B.

The explanation for the correct answer is that we used the principle of heat exchange and the given relation between the specific heats and masses of the substances to derive the equation for the final temperature Tf. We then simplified the equation to get the final expression.